Rings with Generalised Distributive Laws

Some authors [1, 2, 3] have studied algebraic systems which are generalisations of a ring obtained by replacing the usual distributive laws of a ring by more general ones, thus giving the additive identity element a nontrivial multiplicative role. We study here the most general such system called pseudoring, the (m, n) distributive ring of Beaumont [l] and the w-ring of Satio [3] being particular cases of this system.